Tutorial Answers - School of Physics - The University of New South ...

9. [K 4.1]. Calculate the minimum photon energy necessary to dissociate the deuteron i.e.
γ + d → p + n. Take the deuteron binding energy to be 2.224589 MeV and use a nonrelativistic
approach.
Conserve energy and linear momentum:
p
γ
→ E
= p
γ
p
+ p
= [ m
p
n
&
+ m ] c
n
E
2
γ
+ m
⎪⎧
⋅ ⎨1
−
⎪⎩
d
c
2
= m
2md
m + m
p
p
c
n
2
+ K
p
+ m c
+ K
⎪⎫
−1⎬
= 2.226219MeV
⎪⎭
10. [A&M 14.11]. On the basis of tabulated masses, which of the isobars, 17 N, 17 O and 17 F, would
you expect to be the most stable ? Atomic masses are:
17
17
17
M ( N)
= 17.008450 u,
M ( O)
= 16.999131u,
M ( F)
= 17.002095 u,
17 O has the lowest mass and therefore the highest binding energy.
11. [K 5.1] Give the expected shell-model spin and parity assignments for the ground states of (a)
7 Li; (b) 11 B; (c) 15 C; (d) 17 F; (e) 31 P and (f) 141 Pr. [(a) 3/2 and –1; (b) 3/2 and –1; (c) 5/2 and +1;
(d) 5/2 and +1; (e) 1/2 and +1; (f) 5/2 and +1]. See left-hand side of figure 5.6, p123.
n
2
n
( a)
( b)
( c)
( d)
( e)
( f )
Li,
Z = 3, N = 4. p in 1p
7
11
15
31
B,
Z = 5, N = 6. p in 1p
C,
Z = 6, N = 9.
17
F,
Z = 9, N = 8. p in 1d
P,
Z = 15, N = 16. p in 2s
141
n in 1d
3
2
3
2
5
2
5
2
1
2
Pr, Z = 59, N = 82. p in 2d
∴ I = 3/ 2, π = ( −1)
∴ I = 3/ 2, π = ( −1)
∴ I = 5/ 2, π = ( −1)
∴ I = 5/ 2, π = ( −1)
∴ I = 1/ 2, π = ( −1)
5
2
= ( −1)
= ( −1)
= ( −1)
= ( −1)
∴ I = 5/ 2, π = ( −1)
l
l
l
l
l
1
1
2
2
= ( −1)
l
= −1∴
I
= −1∴
I
= + 1∴
I
= + 1∴
I
0
= ( −1)
= + 1∴
I
2
π
π
π
π
=
=
=
π
=
3 −
2
3 −
2
5 +
2
= + 1∴
I
5 +
2
=
1 +
2
π
=
5 +
2
12. [K5.7] Calculate the shell-model quadrupole moment of 209 Bi (I = 9/2 – ). (Experimental value =
–0.37 b).
Q
=
Q
sp
2 j −1
= −
2( j + 1)
⎛
9
2 ⋅ −1⎞
2
3 2
= −⎜
⎟
× × 1.2 × 209
11
2
⎝ ⋅ 5
2 ⎠
r
2
2 j −1
3
= − ⋅ R
2( j + 1) 5
2
3
= −22.13
fm
2
2
2 j −1
3
= − ⋅ R
2( j + 1) 5
= −0.22b
13. [K5.2] The low-lying energy levels of 13 C are: Ground state (1/2–); 3.09 MeV (1/2+); 3.68
MeV (3/2–) and 3.85 MeV (5/2+). Interpret these states according to the shell-model.
13
C , Z = 6, N = 7.
Protons are paired; the energy states of 13 C are determined by the unpaired (7 th ) neutron.
2
0
A
2
3